### Abstract

The Method Of Characteristics (MOC) has been widely used for two dimensional lattice calculations. One of the main drawbacks of the MOC is its poor spatial representation of the within-group energy source, which requires the use of a very fine mesh to adequately resolve the neutron flux solution. The most straightforward way to improve the spatial representation of this source would be to project the scalar flux to a set of higher-order trial functions within each mesh element, but this is expensive. An alternative to this has already been proposed that exploits the angular flux moments on the surfaces of each mesh element. In this paper, we present a new alternative in which we define a higher order representation of the isotropic source. The key feature of our method is the introduction of a new, linear discontinuous source representation that does not resort to an expensive spatial projection. This is accomplished by using a P1 approximation to construct the average derivative of the spatial source. So far, the derivation has been done only for a linear representation of the isotropic sources in two and three-dimensional geometries. The paper presents an analysis of the performance of the new method in simple cases and the Takeda 1 benchmarks.

Original language | English |
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Title of host publication | American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009 |

Pages | 461-473 |

Number of pages | 13 |

Volume | 1 |

Publication status | Published - 2009 |

Externally published | Yes |

Event | International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009 - Saratoga Springs, NY, United States Duration: 3 May 2009 → 7 May 2009 |

### Other

Other | International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009 |
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Country | United States |

City | Saratoga Springs, NY |

Period | 3/5/09 → 7/5/09 |

### Fingerprint

### Keywords

- Linear source
- Method of Characteristics
- Neutron transport

### ASJC Scopus subject areas

- Nuclear Energy and Engineering
- Computational Mathematics
- Nuclear and High Energy Physics

### Cite this

*American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009*(Vol. 1, pp. 461-473)

**Quasi linear representation of the isotropic scattering source for the method of characteristics.** / Rabiti, C.; Palmiotti, G.; Yang, W. S.; Smith, M. A.; Kaushik, D.; Wollaber, A. B.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009.*vol. 1, pp. 461-473, International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009, Saratoga Springs, NY, United States, 3/5/09.

}

TY - GEN

T1 - Quasi linear representation of the isotropic scattering source for the method of characteristics

AU - Rabiti, C.

AU - Palmiotti, G.

AU - Yang, W. S.

AU - Smith, M. A.

AU - Kaushik, D.

AU - Wollaber, A. B.

PY - 2009

Y1 - 2009

N2 - The Method Of Characteristics (MOC) has been widely used for two dimensional lattice calculations. One of the main drawbacks of the MOC is its poor spatial representation of the within-group energy source, which requires the use of a very fine mesh to adequately resolve the neutron flux solution. The most straightforward way to improve the spatial representation of this source would be to project the scalar flux to a set of higher-order trial functions within each mesh element, but this is expensive. An alternative to this has already been proposed that exploits the angular flux moments on the surfaces of each mesh element. In this paper, we present a new alternative in which we define a higher order representation of the isotropic source. The key feature of our method is the introduction of a new, linear discontinuous source representation that does not resort to an expensive spatial projection. This is accomplished by using a P1 approximation to construct the average derivative of the spatial source. So far, the derivation has been done only for a linear representation of the isotropic sources in two and three-dimensional geometries. The paper presents an analysis of the performance of the new method in simple cases and the Takeda 1 benchmarks.

AB - The Method Of Characteristics (MOC) has been widely used for two dimensional lattice calculations. One of the main drawbacks of the MOC is its poor spatial representation of the within-group energy source, which requires the use of a very fine mesh to adequately resolve the neutron flux solution. The most straightforward way to improve the spatial representation of this source would be to project the scalar flux to a set of higher-order trial functions within each mesh element, but this is expensive. An alternative to this has already been proposed that exploits the angular flux moments on the surfaces of each mesh element. In this paper, we present a new alternative in which we define a higher order representation of the isotropic source. The key feature of our method is the introduction of a new, linear discontinuous source representation that does not resort to an expensive spatial projection. This is accomplished by using a P1 approximation to construct the average derivative of the spatial source. So far, the derivation has been done only for a linear representation of the isotropic sources in two and three-dimensional geometries. The paper presents an analysis of the performance of the new method in simple cases and the Takeda 1 benchmarks.

KW - Linear source

KW - Method of Characteristics

KW - Neutron transport

UR - http://www.scopus.com/inward/record.url?scp=74549119480&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74549119480&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:74549119480

SN - 9781615673490

VL - 1

SP - 461

EP - 473

BT - American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009

ER -